F(X+3)=1/F(X)推导到F(X+6)=F(X),类似可得结论怎么推的?好的追20]

设X+3=a
由 F(X+3)=1/F(X) => F(a)=1/F(a-3) => F(X)=1/F(X-3)
设X-3=b
由 F(X+3)=1/F(X)
F(X)=1/F(X-3)
得 F(X+3)=F(X-3),设X-3=c则 F(c+6)=F(c) => F(X+6)=F(X)

F(X+6)=F[(X+3)+3]
令Y=X+3,则 X+6=Y+3
F(Y+3)=1/F(Y)=1/F(X+3)
即F(X+6)=1/F(X+3)
又 F(X+3)=1/F(X)
所以 1/F(X+3)=F(X)
即 F(X+6)=F(X)